fatigue strength and fatigue fracture mechanism for spot ... · pdf filem. shariati and r.m....

2787

Abstract In this paper, the fatigue behavior of the metallic welded U-shape specimens subjected to cyclic loading have been investigated via experimental and numerical analysis. To do so, two sets of the spot welded specimens with different sizes were prepared and fatigue tests were conducted under the various cyclic loads. The crack propagation is numerically examined by using the stress intensity factor values achieved from FE analyses. The modified Paris and Forman–Newman–De Koning models were used to estimate the fatigue crack growth rate. The results indicate that the fatigue life of specimens decreases with any increase in load level. Keywords Crack growth, Fracture mechanics, Finite element, Stress intensity factor, Fatigue life.

Fatigue Strength and Fatigue Fracture Mechanism for Spot Welds in U-Shape Specimens

1 INTRODUCTION

The process of spot welding is widely used to connect the two sheets together particularly in the automotive industries. So far, the fatigue life prediction and modeling of a variety of specimens have been investigated by many researchers (Esmaeili, 2015; Hassanifard, 2014; Mohammadpour, 2014; Chen, 2014; Kang, 2007). Since the area around the nugget is considered as a natural crack or an initial slot, the spot welding is analyzed and its fatigue life is dealt with in fracture mechanics. Ex-perimental results of the analysis and modeling of the spot welding by the concepts of fracture me-chanics play an important role. Because the results of these models must be consistent with the experimental results; otherwise the models are not reliable. One of the studies in which the experi-ments were performed on all samples of spot weld is the study of Adib et al. (2004) that predicted the fatigue life of spot welds using the volumetric method. Sun et al. (2008) studied the effect of the weld junction size and the decline mode on the maximum load and the energy absorption of high-strength steels. Long et al. (2007) investigated the fatigue properties and decline characteristics of

Mahmoud Shariati a,1 Reza Masoudi Nejad a,2 a Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mash-had, Iran 1 [email protected] 2 [email protected] http://dx.doi.org/10.1590/1679-78253094 Received 14.05.2016 Accepted 15.08.2016 Available online 29.08.2016

2788 M. Shariati and R.M. Nejad / Fatigue Strength and Fatigue Fracture Mechanism for Spot Welds in U-Shape Specimens

Latin American Journal of Solids and Structures 13 (2016) 2787-2801

high-strength sheets of spot weld. Choi et al. (2007) studied the fatigue life of steel sheets of ternary spot weld (three sheets on each other). Lin et al. (2006) examined the modeling of fatigue crack growth of spot welds under cyclic loading. Pan et al. (2002) investigated the fatigue life prediction of spot welds under cyclic strain range. Kang (2007) studied the fatigue life prediction of spot welds joints using equivalent structural stress method. Lin et al. (2006) investigated the decline of spot welds with regard to the state of plane stress. Yang et al. (2010) developed a simple model to simu-late the pull-out failure behavior of spot welds in vehicles fractures simulation. The model was vali-dated by modeling the tests performed on the spot weld. Hassanifard et al. (2013) examined the effects of different arrangement of spot welding on fatigue behavior of spot welding joints. Florea et al. (2013) studied the welding parameters affecting the fatigue behavior of spot welding for alumi-num alloy 6061-T6 experimentally. The results of this study revealed that the welding parameters have a great influence on the microstructure and the fatigue life of spot welding joints and alumi-num foil with a thickness of 2 mm.

Nowadays, with developing the analytical and numerical methods in solid mechanics, it is in-tended to study the different parameters both quantitatively and more accurately instead of quali-tative study of their effects. A lot of studies have been conducted using the numerical and analytical methods which have investigated its different aspects. In the literature (Zhang, 1999; Dong, 2001;Hadipour, 2011;MasoudiNejad, 2015, 2016; Moghadam, 2016), some of these issues are studied using some experimental observation, analytical calculations and FEA calculations within various contexts. Most of the previous studies described above have investigated the fatigue behavior of the metallic welded specimens is a discussion which has not been noticed very much. In this paper, the behavior of the crack growth, the fatigue life of U-shape specimens under different level of loadings and the determination of the sheet thickness on the fatigue life have been investigated by finite element method and experimental tests. A three-dimensional finite element method is employed to provide a prediction of fatigue crack growth in the U-shape specimens. Therefore, the various load levels with constant amplitudes on the fatigue life is assessed by using damage mechanic methods. Also, the fatigue crack growth under dynamic loading is simulated in the three-dimensional model by using Franc3D software (Cornell Fracture Group, 2016; MasoudiNejad, 2015). 2 EXPERIMENTAL PROCEDURES

The materials, which have been used in this study, are the two sheets of U-shape specimens with 1 mm and 1.5 mm thickness, manufactured from ST37 steel whose mechanical properties have been summarized in Table 1. The standard tensile tests of tension of metallic materials, E8, are per-formed to determine the stress-strain diagram according to ASTM standards. The true stress–strain plot of the used material has been illustrated in Figure 1.

Elongation (%) Poisson’s ratio Tensile strength

(MPa) Yield stress

(MPa) Young’s modulus

(GPa)

45 0.33 340 260 210

Table 1: Mechanical properties of ST37 steel.

M. Shariati and R.M. Nejad / Fatigue Strength and Fatigue Fracture Mechanism for Spot Welds in U-Shape Specimens 2789


Figure 1: True stress–strain curve of ST37 steel.

Three types of U-shape specimens with different thickness are used in this investigation. The

dimensions of test specimens have been illustrated in Figure 2. As shown in the Figure 2 the U-shape specimens with two sheet thickness of 1 by 1mm, 1 by 1.5mm and 1.5 by 1.5mm are weld jointed together. At least 5 specimens of each type under different loading with constant amplitude conditions are used. The specimen’s were provided by means of a pedal spot welding apparatus. The condition of welding is as followings:

Current welding : 8 KA Welding time : 3 seconds Electrode face diameter : 4-6 mm Material : mild Steel As the sheets with two different thicknesses are used the U-shape specimens are divided in two

different groups. The specimens are introduced in the form of: UA**-**-*. Where UA and UB refer to the type of specimens with 4mm and 6mm diameter respectively; the first two digit numbers from the left side indicates the thickness size of Sheets. The third number refers to the number of specimen in each series. In this investigation, each series have 5 specimens at least. The experi-mental tests have been conducted with stress ratio of 0.01 and frequency of 10 Hz using servo-hydraulic INSTRON 8802 machine. In each case, several fatigue tests were performed with different maximum applied longitudinal loads. Figure 3 shows the experimental test setup.

Figure 2: U-shape specimens’ configuration and dimensions (in mm).



Figure 3: Experimental test setup.

3 FAILURE ANALYSISUNDER FATIGUE TEST

In general, two types of failure are observed in U-shaped samples: 1. Nugget Fracture: This type of fracture occurs because of the small nugget diameter or large

applied force. This fracture occurs at the interface of between the nugget and the two joined sheets. If the applied force is greater than the spot weld endurance, the decline will occur suddenly without crack growth in joined sheets (Figure 4-a), but if the applied force is lower than the spot welded endurance and strength, first the crack will grow slightly (about 1 to 2 mm) and then will fail.

2. Nugget Pull-Out: In this type of fracture, first the crack growths fully in the sheet thickness and then after reaching the sample surface and significant growth in the sample width the nugget will be pulled out and then the failure will occur due to the decrease of sample strength. (Figure 4-b).

(a) (b)

Figure 4: Nugget pulled out on applying at extreme loading (a) failure occurs before

crack growth (b) failure occurs after a gradual growth.

Figure 5 shows the UB15-15-4 specimen in which the thickness of both sheets is 1.5 mm and is

affected by the maximum force of 900 N and endured 202,730 loading cycles. As can be seen, the



crack is occurred in both sheets but it grew more only in one of them and the crack passed the sample width largely.

Figure 6 shows the UB10-15-2 specimen when the thickness of one of the sheets is 1 mm and the other one is 1.5 mm and is affected by the maximum force of 650 N and endured 15922 loading cycles. As can be seen before the crack can grow in it, the thinner sheet (left) was torn while the thicker sheet received no damage.

Figure 7 shows the UB10-10-1 specimen in which the thickness of both sheets is 1 mm and is af-fected by the maximum force of 650 N. As can be seen before the crack can significantly grow in sheets, both sheets were torn due to the thinness.

Figure 5: Crack growth path in U-shape specimens.

Figure 6: Crack growth path in UB10-15-2 specimen.

Figure 7:Crack growth path in UB10-10-1 specimen.



Figure 8 shows the UB15-15-2 specimen in which the thickness of both sheets is 1.5 mm and is affected by the maximum force of 650 N and endured 342881 loading cycles. It can be seen from Figure 8 that the crack grew significantly in one of the sheets but no crack can be seen in the other sheet. The fatigue life graphs for each of the two types of U-shape specimens with different thick-ness are shown in Figure 9. The life pertains to all of the three steps of fatigue as initiation, propa-gation and the fracture of the fatigue for specimen.

Figure 8: Crack growth path in UB15-15-2 specimen.

The most majority part of the fatigue crack growth at the spot weld and its propagation to the

surface of a specimen which cannot to observed. Since the crack growth behavior can be investigat-ed exactly as it clearly appears at the surface, an optical microscope with magnification factor of 100 is used to measure the fatigue crack length at the various loading levels. In order to see the fatigue crack growth obviously the surface of all parts around the nugget were smoothly polished. Also during the loadings, the crack length was measured accurately on the surface of specimens by means of lines that was created by a precision coulisse in 1mm distance from each others.

In Figures 10-11, some images of the crack growth on the surface of U–shape specimens are dis-played. Some snapshots for crack growth path relating to UA15-15-1specimen during observation at the surface are shown in figure 10. Also snapshots for crack growth path relating to UA10-10-2specimen during observation at the surface and the final fracture are shown in figure 11. Figure 11-d reveal that complete fracture occurs as quickly as the cracks are observed at the specimen’s sur-face.

Figure 9: Load-fatigue life curves for U-shape specimens.



(a) (b)

Figure 10: Stepwise snapshots for crack growth path of UA15-15-1 specimen during

observation at surface after (a) 1,365,000 cycles (b) 1,400,000 cycles.

(a) (b)

(c) (d)

Figure 11: Stepwise snapshots for crack growth path of UB10-10-2 specimen during observation at surface

and complete failure after (a) 230,000 cycles (b) 260,000 cycles (c) 300,000 cycles (d) 325,890 cycles.

4 FINITE ELEMENT SIMULATION

The result of numerical analysis for the U-shape specimens have been done by software named Franc3D (Cornell Fracture Group, 2016; MasoudiNejad, 2015) which is a software for 3D finite element analysis and especially for studies on crack growth in two dimensional geometries. This software is supplied by the researchers of Cornell University and distributed to the public. This software is able to use the different equations of fatigue crack growth in order to predict the lifetime of the specimen under fatigue loads. Also, at this software the debates which are related to the de-struction as a result of the net-section stress of profile at presence of the crack for the lifetime pre-diction of the section have been discussed.



In figure 12-a the finite element of the U-shape specimen and the existed crack in it have been illustrated which more elements are used to obtain better results around the crack and the place of contact loading imposing. In this study the crack geometry for the crack has been considered semi-elliptical for the crack (figure 12-b). The reason of this form of cracks is the comprehensiveness and field observation in experimental tests. The dimensions of the investigated crack are b=0.4 mm, and a=0.2 mm which are as the initial crack and for the crack illustrated in figure 12-a.

(a) (b)

Figure 12: Mesh generation of U-shape specimen for finite elements analysis

(a) specimen without any crack (b) specimen with crack.

Linear elastic fracture mechanics (LEFM) is a suitable method for linking data to fatigue crack

growth because it describes the stress conditions at the crack tip using only a parameter, i.e. the stress intensity factor. The calculated path is achieved using Maximum Tangential Stress, Maxi-mum Energy Release Rate and Strain Energy Density criterions. Such calculations are carried out in each step of the crack growth. Since proposed path in three criteria have not significant differ-ences, and the use of maximum tangential stress is recommended by FRANC3D software providers, it is used to determine the angle of crack growth (MasoudiNejad, 2013, 2014). The crack tip curve can be fit after determining the direction of crack growth. In continue, crack growth can be simu-lated for another step. After crack growth, Specimen is meshed again and be prepared to solve. This is repeated for each step until the rate of growth is expected. Figure 13 shows crack after 10th stage of growth. Two Fatigue crack growth rate models were used in this study.

Figure 13: Crack after 10 stages growth.



4.1 The Modified Paris Model

Modified Paris model is used to calculate crack growth rate and fatigue life. Modified Paris model considers the effects of closure of the crack. The growth rate is defined by the equation as follows (Anderson, 1994):

max( )n neff op

daC K C K K

dN (1)

where effK , the effective stress intensity factor is defined as the difference between the maximum

mode I stress intensity factor ( maxK ) and stress level where the crack first opens( opK ) and C, n are

material constants. 4.2 Forman–Newman–De Koning Model

The FNK fatigue model is expressed as (Newman, 1984):

max

111

1

pth

n

q

crit

K

da f KC K

dN R K

K

(2)

In the above equation, a and N are the crack length and the number of applied fatigue cycles.

C, n, p and q are empirical constant derived by curve fitting the test data R is the load ratio, K is stress intensity factor, maxK is the maximum applied stress intensity factor range, critK is the critical

stress intensity factor range for unstable crack growth, thK is threshold stress intensity factor and

f is described in order to keep into account the plasticity-induced crack closure:

2 30 1 2 3

0 1

0 1

max ; 0,

2 02 2

R A A R A R A R for R

f A A R R

A A R

(3)

Here,

1

2 max0

max1

2 0 1 3

3 0 1

0.825 0.34 0.05 cos ,2

0.415 0.071 ,

1 ,2 1.

F

F

A

A

A A A A

A A A

(4)



where max F and are the plain stress/strain constraint factor and the ratio of the maximum

applied stress to the flow stress, respectively. 5 COMPARISON OF PREDICTED RESULTS AND DISCUSSION

The comparison between the predicted fatigue lives and the experimental lives has been illustrated in Figures 14–18 for welded U-shape specimens. It can be seen from Figure 14 that for UA10-15-2 specimen, the Paris model agrees with the experimental tests results very well. However, estimated fatigue lives by means of FNK model were overestimated.

The comparison between the estimated fatigue lives using fatigue models and experimental tests for UA15-15-4 specimen is shown in Figure 15. The FNK model estimates the fatigue life very accu-rately for this specimen. But, the Paris model does not estimate the fatigue life as accurate as FNK model for this specimen.

The comparison between the estimated fatigue lives using the Paris and Forman–Newman–De Koning models and the experimental lives for UB10-10-2 specimen is illustrated in Figure 16. Ac-cording to the Figure 16, the Paris model is able to estimate fatigue life with sufficient level of accu-racy for this specimen.

The comparison of tested fatigue lives with the predictions by the Paris and Forman–Newman–De Koning models is shown in Figures 17-18. The result shows that the FNK can reasonably pre-dict the fatigue lives of the UB10-15-1 specimen. However, there is a significant deviation between test and predicted fatigue lives for UB10-15-1 specimen and UB15-15-4 specimens.

In accordance with Figs. 14–18, the FNK model covers all three regimes of crack growth rate diagram (from threshold to unstable crack growth) on the basis of stress intensity factor. Besides that, Paris model is acceptable for the two regimes of the mentioned diagram. So it is expected that fatigue life which is predicted using FNK model has a good agreement with experimental results. The comparison between the estimated fatigue lives using the Paris and Forman–Newman–De Kon-ing models and the experimental lives for A-type and B-type specimens are given in Tables 2 and 3, respectively.

Figure 14: Comparison between the estimated and experimental fatigue tests for UA10-15-2 specimen.



Figure 15: Comparison between the estimated and experimental fatigue tests for UA15-15-4 specimen.

Figure 16: Comparison between the estimated and experimental fatigue tests for UB10-10-2 specimen.





Specimen life

(cycles) Crack length in total

cycle numbers (mm)

Maximum applied load

(N)

Kind of U-shape specimens FNK model

predictions Paris model predictions

Test data

1689016 1211981 1335255 4 200

1mm-1mm 509873 411235 458463 25 350 136098 96052 116335 23 500 19681 15334 17557 11.5 650

1645903 1210845 1335000 6 200

1mm-1.5mm 412356 302187 333182 18 350 77867 56926 60933 18 500 16980 11093 13549 7.5 650

1761309 1347892 1434000 25 500

1.5mm-1.5mm 430921 314756 342881 15 650 181304 130982 156592 18.5 800 126895 101516 113435 10.5 900

Table 2: Fatigue test and FEM results on the A-type specimens for R=0.01.

Specimen life (cycles) Crack length in total

cycle numbers (mm)

Maximum applied load

(N)

Kind of U-shape specimens

FNK model predictions

Paris model predictions

Test data

161031 118930 1308816 6.5 200 1mm-1mm 454758 311478 325890 24.5 350

71023 49765 53766 8.5 500 1547002 1117385 1238900 10 275

1mm-1.5mm 592070 419908 460135 20 350 79653 53491 58338 11 500 19165 13116 15922 8 650

1518750 1092732 1199346 2.5 500

1.5mm-1.5mm 721348 423841 584243 7 650 378613 221950 240411 8 800 269282 193728 202730 19 900

Table 3: Fatigue test and FEM results on the B-type specimens for R=0.01.



According to the experimental results, the crack life can be observed in the stages of initiation and crack growth between the sheet thicknesses (until the visibility of crack at the sample surface that could be observed when its length was about 2 mm). Due to the these results, it is indicated that in specimens with high lifetime (low applied load) the stages of crack initiation and growth include more than half of the final lifetime; while in specimens with low lifetime (high applied load), the stages of crack initiation and growth include about 40 percent of the final lifetime of the speci-mens.

Cracks reach the external surface suddenly when they are fully grown so that the measurement of micro cracks (less than 2 mm) is not possible using the tool. In general, when cracks appear on the external surface, they have a length about 2.5-4 mm. Also, the location of the crack is in the external surface, around the nugget and the vertical edge.

According to the experimental results, the relationship between the type of failure and the life-time can be realized. In general, the higher lifetime increases the sudden failure and the spot weld failure. Also, in all displacement curves based on the number of loading cycles, in the low number of course, the slope of the curve is almost constant and close to zero. But after a number of loading cycles (which is different for each sample according to its thickness and loading) the slope of the curve increases. In fact, this spot can be considered almost the same spot that started the crack initiation. 6 CONCLUSIONS

In this paper, the fatigue behavior of the metallic welded U-shape specimens subjected to cyclic loading have been investigated via experimental and numerical analysis. The following results have been obtained from the observations and analysis of the surfaces and the fracture sections:

1. The initiation and the fatigue crack growth first occurs in U-shape specimen having small thicknesses in which the crack length is longer.

2. In U-shape specimens with the same thicknesses, crack appears in both sheets with an ap-proximately the same length.

3. Due to stress concentration at the vicinity of the nugget, crack grows around it as an arc shape and the fracture occurs at the sheet rather than the nugget.

4. The majority portion of the fatigue life of spot welds relates to the initiation and the crack growth to the specimen’s surface.

5. Since in high loading level, the nugget is pulled out after a small crack growth, the fatigue life of specimens decreased with any increase in loading. However, in low loading level, the crack grows significantly.

6. The results of three-dimensional finite element analysis have been compared with those achieved from experimental tests. The numerical analysis results obtained show good agree-ment with those obtained from experimental results.

7. Among the applied model, the FNK model has the best accuracy for all types of the speci-mens.

8. The modified Paris model shows rather inaccurate prediction of fatigue life among the em-ployed fatigue model for fatigue strength of spot welded U-shape specimens investigated in this paper.



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